I'd say $200-300. For open back I'd aim for HD650s. From what I've seen they have neutral frequency response, low distortion, and excellent decay. Those usually go for more like $400 though and require a good amp. In that same performance bracket you have the DT990 pro and Q701/K701 which both go for about $200. Those all have low distortion and great decay, but need a little bit of an equalizer to be neutral. The DT990 need to be cut by ~4-6dB from 4-9kHz. The Q701 and K701 need the midrange to be cut a bit (around 1kHz if I remember correctly). I believe the q and k versions are basically the same headphone. Note that the consumer version of the DT990 are $100 more and from what I've read the band is looser (more comfortable) and come in a 600 ohm version which is marginally better. It's up to you if you want to spend an extra 50% on marginally better comfort and marginally better sound that will require a more powerful amp.
Closed back is a little bit more difficult. There's the M50x for $150, the DT770 for $200ish. And not much else. I know there's a few more but I don't have enough knowledge of them to recommend them (shure etc).
I own the DT990 pros and they sound great. They need an amp to get to medium to high volume just like the HD650/Q701/K701 will need. They are extremely comfortable and are built really well. And they sound great. If you look up reviews you'll read they are fatiguing. That doesn't mean the treble is bad. It is very clean and has excellent decay, it is just too loud. Cut from 4-9kHz by a few dB with an equalizer and you'll be golden.
I also own the ATH-M50's and have for about 5-6 years. They do not need an amp and are built like a tank. The pleather will start to flake after 6-18months depending on how much you abuse them. Lots of people say an amp will improve some intangible quality of the sound. That is ********. It makes it louder, no more no less. You don't need an amp unless it's too quiet. You may need an amp if you plug them into a ****ty phone or something in which case the SNR will make them sound like **** even with an amp. I own the old version of the M50s. But I would go with the M50x or the DT770 if I were you. The M50x have flatter bass than the original M50s and a removable cable which is nice. The DT770 will leak more sound than the M50x from what I've read, and I believe it is due to the velour pads. However, the M50's have pleather pads which are uncomfortable after about 4ish hours, and they soak up sweat and harden over time. Over time they will start to crack. There is no solution to this problem without losing the excellent sound isolation. They leak much more sound with velour pads, and usually need an EQ with those pads (shure 940 pads work, but leak sound and need ~5kHz cut by a few dB). Stock M50's don't need to be EQ'd IMHO. I don't know if the M50x pads solve that issue, I suspect they're better as they're different from what I've heard, but I doubt they've solved that problem.
That is what I can recommend based on my experience. I'll also recommend the HD650 over the DT990 based on measurements I've seen. Although the DT990 are basically on par after being EQ'd. The AKG's are also on par (after EQ) from the measurements I've seen. I can also vouch for the M50s. Although they don't hold up to the DT990's as far as sound quality, they surpass it in portability and isolation. It just depends on what is important to you.
Note that there are many MANY headphones I will not recommend based on measurements I've seen. For instance, the DT880 have worse harmonic distortion based on measurements I've seen and reading between the lines of reviews I've read. Even though their frequency response is flatter, I'd recommend the DT990's over them. Frequency response can be fixed. Distortion can't. Also, there are so many high end headphones with terrible decay. By that I mean there are certain places in the treble that ring like a bell. That will make the cymbals etc all blur together. That is not acceptable in a high end headphone, and since many people do not think about transient response that aspect goes overlooked. I can vouch that the M50 and DT990 both have excellent transient response. In general open back headphones have better transient response although not always. The M50's are an exception to that rule. I've also seen measurements that indicate the HD650 and Q701/K701 have excellent transient response as well.
Hope this helps you. Sorry I wrote so much, but I hope my experience helps you. If you have any questions I can help you with just ask. Also, I'm a little drunk, I'll end this before it turns into a novel.
